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This does sound correct. New York uses all of your income (earned in all states) to determine your tax bracket and tax, and then apportions out the percentage of the tax attributed to your NY state income, rather than parsing out the income itself.
For example, if you earn $80,000 in NJ and $20,000 in NY you'll see $100,000 as your income on the state return, but you won't see the same tax as someone who earned $100,000 in New York.
If the NY tax on $100,000 would then be $5,000, you'd be charged only $1,000 or 20% of that tax, because only 20% of your income was earned in NY.
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